On the number of kth powers inside arithmetic progressions

2018/11/29 by Jean Bourgain, Ciprian Demeter, Bourgain, Jean +1
Mathematics · #Advanced Mathematical Identities #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1811.11919

openalex publication_date 2018/11/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We find upper bounds that are sharp for the number of kth powers inside arbitrary arithmetic progressions whose step has O(1) many divisors.

Related

• A comment on the number of k-th powers inside arithmetic progressions
• Arithmetic progressions of squares, cubes and n-th powers
• Arithmetic progressions among powerful numbers
• Squares in arithmetic progression over number fields
• Arithmetic Progressions in Squarefull Numbers